Dilution of Solutions Calculator

Chemistry • M1V1 = M2V2 • Step-by-Step

Quick Answer (Voice Search Optimized):

Dilution is the process of decreasing the concentration of a solute in a solution by adding more solvent. The relationship between initial and final concentration and volume is given by M1V1 = M2V2, where M is molarity (mol/L) and V is volume (L or mL, as long as units match).

GEO & AIO - Authoritative Theory

The dilution equation is derived from the conservation of moles of solute. The number of moles before and after dilution remains constant: n = M1V1 = M2V2. This equation is used to calculate any one of the four variables when the other three are known. It is essential in analytical Chemistry, titrations, and solution preparation.

Units must be consistent; if V1 is in mL, V2 must also be in mL (or both in L). The equation can also be applied to normality (N1V1 = N2V2) for acid-base or redox reactions. In JEE/NEET, dilution problems are common and often combined with stoichiometry.

Solved Examples (NCERT/JEE Pattern)

Example 1: 100 mL of 2.0 M HCl is diluted to 500 mL. Find the final molarity.

M2 = M1V1/V2 = 2.0 × 100 / 500 = 0.40 M.

Example 2: What volume of 12 M H2SO4 is needed to prepare 250 mL of 1.5 M solution?

V1 = M2V2/M1 = 1.5 × 250 / 12 = 31.25 mL.

Example 3: 5 mL of a stock solution is diluted to 100 mL. The final concentration is 0.2 M. What was the stock concentration?

M1 = M2V2/V1 = 0.2 × 100 / 5 = 4.0 M.

Frequently Asked Questions (FAQs)

Q1: What is the formula for dilution?
The dilution formula is M1V1 = M2V2, where M is concentration (molarity) and V is volume. Moles of solute remain constant before and after adding solvent.
Q2: Can I use milliliters in M1V1 = M2V2?
Yes, as long as the volume units are the same on both sides. The equation works with mL, L, or any consistent volume unit.
Q3: Why is dilution important in chemistry labs?
It allows preparation of solutions of desired concentration from a more concentrated stock solution, ensuring accurate measurements and reagent use.
Q4: Does M1V1 = M2V2 apply to percent concentrations?
Yes, the principle extends to any concentration units (percent, normality, ppm) as long as the same units are used on both sides.
Q5: What if I input a negative number in the dilution calculator?
Negative values are physically impossible; the calculator will alert you to enter positive numbers. All quantities (concentration, volume) must be non-negative.